The figure above illustrates how thermoelectric couples can be used to either perform refrigeration or generate electrical power from waste heat. It is taken from a nice Perspective in Science Smaller is Cooler by Brian Sales which reviews state of the art materials in 2002.

The thermoelectric figure of merit, ZT is a dimensionless ratio which is a good measure of how useful a material will be in thermoelectric applications.

sigma is the conductivity and kappa the thermal conductivity.

Currently used materials such as Bi2Te3 [also a topological insulator!] have values of ZT ~1. If materials can be found with ZT~4 then thermoelectric refrigerators will be competitive with traditional compressor refrigerators, which are less reliable and environmentally dirtier.

It is important to note that the thermal conductivity is the sum of electronic and phonon contributions. If one neglects the latter (for the moment) and uses the Wiedemann-Franz ratio then ZT ~ S^2 where S is in units of k_B/e. This is indeed its magnitude near the coherence temperature in strongly correlated electron materials. Hence, ZT ~ 1 (but not larger) seems possible.

BUT, this argument neglects the thermal conductivity due to phonons which is much larger that the electronic contribution in this temperature regime. So one needs to find a way to reduce this. This leads to the idea of a Phonon Glass Electron Crystal.

Here are a few choice from Lightman's article quotes I found debatable:

Dramatic developments in cosmological findings and thought have led some of the world’s premier physicists to propose that our universe is only one of an enormous number of universes with wildly varying properties, and that some of the most basic features of our particular universe are indeed mere accidents—a random throw of the cosmic dice. In which case, there is no hope of ever explaining our universe’s features in terms of fundamental causes and principles...Theoretical physics is the deepest and purest branch of science. It is the outpost of science closest to philosophy, and religion....

Theoretical physicists are Platonists. Until the past few years, they agreed that the entire universe, the one universe, is generated from a few mathematical truths and principles of symmetry, perhaps throwing in a handful of parameters like the mass of the electron. It seemed that we were closing in on a vision of our universe in which everything could be calculated, predicted, and understood....

We are living in a universe uncalculable by science....

The most striking example of fine-tuning, and one that practically demands the multiverse to explain it, is the unexpected detection of what scientists call dark energy.

Perhaps rather than giving up on theoretical physics better options may be to

give up on Platonism,

give up on reductionism,

give up on unbridled philosophical speculation

be a little humbler and be open to the idea that there may be some new physics to be discovered in the particle physics Desert which covers 12 orders of magnitude in energy!

Friday, January 27, 2012

The plot below is an important one which I have been meaning to blog about for a while. It shows the strength of the diamagnetic signal [increasing from blue to purple to red]

from an underdoped cuprate superconductor as a function of magnetic field H and temperature T.

The figure is taken from a paper from Ong's group, discussed in an earlier post.
The superconducting transition temperature Tc is 12 K. However, a magnetic field of about 45 tesla is required to destroy the diamagnetic signal which is associated with Cooper pairing. Furthermore, this "upper critical field" H_c2 is weakly temperature dependent. This large field scale reflects the large binding energy of the Cooper pairs. This can be seen by converting H_c2 to a coherence length (~30 A) and then an energy gap (~20 meV ~ 200 K) via a Pippard type formula [see this earlier Science paper by Ong et al.]. The energy gap is comparable to the pseudogap seen in ARPES and much smaller than k_B Tc.

Wednesday, January 25, 2012

There is an interesting article Ultracold Bose gases deviate from the textbook picture in the Search and Discovery section of the July 2011 Physics Today. [My issue just arrived by snail mail today!].
It discusses how recent experiments have quantified deviations from the non-interacting boson theory of Einstein, which is taught to undergraduates.
It seems that these deviations can be described by Hartree-Fock theory. One might argue Hartree-Fock is also rather "text book".

For all the hype, somehow I cannot get excited about atomic BECs. To me, there seems a distinct contrast to solid state systems such as strongly correlated electron materials which exhibit properties (high-Tc superconductivity, spin liquids, heavy fermions, pseudogap, non-Fermi liquid metals,...) which are such a long way from anything remotely "text book"-ish and whose explanation requires the development of new physical concepts, approximation schemes, and numerical methods.

Diamagnetic response of the superconducting state is orders of magnitude larger than other states of matter. [Due to the Meissner effect superconductors are sometimes said to be perfect diamagnets]. A state with no long range superconducting order but large fluctuations can produce a significant diamagnetic response. The authors find that for a wide range of underdoped cuprates that there is significant diamagnetism for a wide temperature regime above Tc. Moreover, this signal co-exists with a large Nernst signal.

This is important because it tends to rule out a proposed alternative explanation for the large Nernst signal that it could be produced by quasi-particles in small hole pockets associated with a density wave state.

A key signature of superconducting fluctuations is a non-linear dependence of the magnetisation on the magnitude of the magnetic field. For small fields it must be linear in field, but there must be some field scale, of the order of the upper critical mean-field H_c2 above which there is no diamagnetic response. This means there is some field scale H_min at which the magnetisation is a minimum. The non-linearity of the field dependence is seen in the Figure below. (The different curves correspond to different temperatures).

The Nernst signal shows a similar non-linear field dependence (see this PRB). The authors argue that if it is due to quasi-particles it should be linear in field up to a much higher field scale, e.g. comparable to the band width.

Aside: Are there any measurements of non-linear diamagnetism on organic charge transfer salts?

Monday, January 23, 2012

Metamagnetism occurs when the magnetic susceptibility increases with increasing magnetic field. This generally does not occur in weakly interacting systems. For example, if the susceptibility is enhanced by magnetic fluctuations, these are generally decreased by a magnetic field. However, DMFT calculations show this can occur for intermediate coupling. This is discussed in detail in the following paper:

In a Fermi liquid picture the susceptibility can either increase due to an increase in the effective mass or increase due to the quasi-particle interaction F0a (the Landau Fermi liquid parameter which determines the Sommerfeld-Wilson ratio).

Possibly the most promising candidate material for some of this physics is CeRu2Si2. The susceptibility increasses by a factor of more than 8, whereas the specific heat coefficient gamma only increases by a factor of 1.6.

Friday, January 20, 2012

Conical intersections [where the potential energy surfaces of two electronic states touch] are ubiquitous in photochemistry. Their most important role is that they can explain why some photochemical reactions proceed so fast (i.e, on the scale of 10's of femtoseconds). However, an important outstanding question is:

Does the Berry's phase [geometric phase] associated with the conical intersection [CI] have important observable consequences?

There is a nice 2005 Perspective in Science by David Clary which discusses this for the specific case of the simplest possible chemical reaction H2 + H to H + H2. It seems that [contrary to what was claimed in the 90's] molecular scattering experiments associated with the ground state surface below are not sensitive to the geometric phase due to cancellations of terms associated with different angular momentum channels. However, showing this cancellation is rather subtle!

Aside 1 : the CI here arises due to the degeneracy of the E irreducible representation associated with the C_3 symmetry of the transition state which occurs when the three H atoms form an equilateral triangle.

Wednesday, January 18, 2012

Solid state physics text books tell us that Matthiessen's rule is obeyed by simple metals: the temperature dependent resistivity is the sum of a temperature independent term due to elastic scattering off impurities and an impurity independent term which is temperature dependent due to inelastic scattering. I teach this to undergrads, but have struggled to actually find experimental data to show them.

Yesterday I came across a 1944 paper by Fairbank which contained the figure below for copper with tin impurities:

It looks pretty convincing. However, the text points out that the temperature dependence actually varies significantly with the impurity concentration, in violation of Matthiesens rule!

I am currently writing a grant application. This is hard going even for old hands. The most irritating bit is all the messing around with formats and fonts. As to text I find the best strategy is like for most writing: just get something (almost anything!) down on paper and then rewrite and polish. This first step is the hardest.

Monday, January 16, 2012

Last week there was an excellent Op-Ed piece in the New York Times, Research Bought, Then Paid For, by Michael Eisen. It is critical of a Bill before the U.S Congress which would stop the current policy of research results from National Institute for Health funded research being available free to the general public. Apparently publisher commercial journals have lobbied for the bill as they see it a way to increase their revenues. The following paragraph is particularly poignant:

the journals receive billions of dollars in subscription payments derived largely from public funds. The value they say they add lies primarily in peer review, the process through which works are assessed for validity and significance before publication. But while the journals manage that process, it is carried out almost entirely by researchers who volunteer their time. Scientists are expected to participate in peer review as part of their employment, and thus the publicly funded salaries most of them draw through universities or research organizations are yet another way in which taxpayers already subsidize the publishing process.

Eisen makes the radical proposal:

Researchers should cut off commercial journals’ supply of papers by publishing exclusively in one of the many “open-access” journals that are perfectly capable of managing peer review (like those published by the Public Library of Science, which I co-founded). Libraries should cut off their supply of money by canceling subscriptions.

Saturday, January 14, 2012

Advocates of the highly speculative notion of "quantum biology" like to invoke the case of superconductivity as a "proof of principle" that macroscopic quantum effects can play a role in biology.

In 1994, Phil Anderson wrote a devastating critique of Roger Penrose's book Shadows of the Mind: A search for the missing science of consciousness. Anderson's review was entitled Shadows of Doubt, and contains the following relevant paragraph:

The review is also reprinted in More and Different. The preamble states the Penrose Fallacy: "all problems too difficult to be solved by the great brain of the author must be identical." (p. 186)

They argue that the density dependent metal-insulator transition seen in Silicon MOSFETs and other two dimensional electron gases (2DEGs) in semiconductor heterostructures is not driven by disorder (which has been claimed for many years) but rather by electronic correlations. Furthermore, the relevant experimental data can be described by a Dynamical Mean-Field Theory (DMFT) treatment of the Wigner-Mott transition in an extended Hubbard model on a lattice.

This means that the non-monotonic temperature dependence of the resistivity is associated with the crossover from a Fermi liquid at low temperatures to a bad metal at higher temperatures. I think thermopower measurements may be the most effective way to test this claim (see an earlier post).

The figure below shows the temperature dependence of the thermoelectric power for the title compounds. Note that it non-monotonic, being linear at low temperatures, reaching a maximum magnitude of order k_B/e ~ 80 microV/K at a temperature T_min.

The next figure shows that T_min (left scale) is correlated with the single ion Kondo temperature (horizontal scale) and the temperature at which the resistivity is a maximum (right scale).

The magnitude of the linear temperature dependence at low temperatures is simply related to that for the specific heat (see also this earlier post) as shown in the Figure below.

Aside: the inset on the lower right considers the Kadowaki-Woods ratio but does not make use of recent work concerning its universality.

All of the above features seem to be characteristic of broad classes of strongly correlated electron metals, as emphasized by Jaime Merino and I, in a PRB published in 2000. The temperature scales in the middle figure are characteristic of that at which there is a crossover from a Fermi liquid at low temperature to a bad metal at higher temperatures.

Wednesday, January 11, 2012

Spend the first half hour of each day thinking and writing in a notebook about the important science questions I am interested in and want to try and answer. And, specifically coming up withmultiple alternative hypothesesand devising ways to distinguish them.

I tried hard but found this very difficult, more than I thought. The tyranny of the urgent often takes over and makes even carving out half an hour at the beginning of each day difficult. Maybe I have done this on 2-3 days per week (on average) over the past two years. However, the multiple alternative hypothesis bit is extremely hard, much harder than just carving out the time. I am hard pressed to think of a single example where I have successfully done this, to the level of actually being able to rule out one alternative hypothesis. On the other hand, I do feel the struggling process is sharpening my scientific thinking.

I welcome others to take up this challenge and let me know how they do! After all, surely this is really what good science is about.

Saturday, January 7, 2012

Shockley called his method of thinking "try simplest cases". But that is really what many good theoretical physicists do when confronted with a complex problem; they try to find a simple model. Only Shockley elevated it to a mantra. He could see his way through the first few stages of any problem very quickly, but he rarely employed his talents to look further below the surface or to check his models against reality. Those who had this ability - for whom Shockley undoubtedly had a good eye - would almost inevitably go off on their own because Shockley could never allow them to follow their own instincts. He saw them as competition and a threat to his authority. I know, because it happened to me in a small way in 1950, and, like others, I survived and may have been the better for it.

.... What comes out of the book well is Shockley's importance. He arguably saved Britain from the U-boats during the battle of the Atlantic. He is certainly the true father of the age of silicon. He is even the inventor of the graphite-moderated nuclear reactor. Yet the public will remember his name as that of the nutty Nobellist who donated his sperm to a genius bank. Who would not want to hear his whole story?

Friday, January 6, 2012

I am told one of the most common (and least kept) New Year's resolutions is to "tame the bulge", i.e. diet and exercise. That is not my subject. Rather, it is taming the academic bulge of every expanding papers, reports, filing cabinets, books, and book cases. Of course, those who do everything electronic do not have to worry about this. It is all on their laptop or iPad. I am not there yet. How do I cope? Not well, but there is a simple rule I have been following at both home and work the past few years that seems to be helping.

Do not buy any new filing cabinets or book cases.

Hence, whenever one buys a new book (or two or three) one has to throw out or give away one (or two or three).

Similarily, when one wants to force new files into a filing cabinet one is forced to throw away some old ones. It is amazing actually how easy this is.

I agree with Anderson's concerns, but offer one minor disagreement about the title and context of his essay. It was meant to be a response to Eugene Wigner's famous essay "The unreasonable effectiveness of mathematics in the natural sciences". However, I think Wigner's paper was wrestling with profound philosophical questions not singing the praises on a highly mathematical approach to theoretical physics.

On the other hand, Phil said he embarked on the exercise "with a very negative attitude" and with his "usual determination to put the cat among the pigeons" due to his difficult relationship with his Princeton colleague Wigner. (This is described at several points in the book.)

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About Me

I have fun at work trying to use quantum many-body theory to understand electronic properties of complex materials.
I am married to the lovely Robin and have two adult children and a dog, Priya (in the photo). I also write an even more personal blog Soli Deo Gloria [thoughts on theology, science, and culture]

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Although I am employed by the University of Queensland and funded by the Australian Research Council all views expressed on this blog are solely my own. They do not reflect the views of any present or past employers, funding agencies, colleagues, organisations, family members, churches, insurance companies, or lawyers I currently have or in the past have had some affiliation with.

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